Question: Simplify the following expression: $\dfrac{45k^2}{90k^5}$ You can assume $k \neq 0$.
$ \dfrac{45k^2}{90k^5} = \dfrac{45}{90} \cdot \dfrac{k^2}{k^5} $ To simplify $\frac{45}{90}$ , find the greatest common factor (GCD) of $45$ and $90$ $45 = 3 \cdot 3 \cdot 5$ $90 = 2 \cdot 3 \cdot 3 \cdot 5$ $ \mbox{GCD}(45, 90) = 3 \cdot 3 \cdot 5 = 45 $ $ \dfrac{45}{90} \cdot \dfrac{k^2}{k^5} = \dfrac{45 \cdot 1}{45 \cdot 2} \cdot \dfrac{k^2}{k^5} $ $\phantom{ \dfrac{45}{90} \cdot \dfrac{2}{5}} = \dfrac{1}{2} \cdot \dfrac{k^2}{k^5} $ $ \dfrac{k^2}{k^5} = \dfrac{k \cdot k}{k \cdot k \cdot k \cdot k \cdot k} = \dfrac{1}{k^3} $ $ \dfrac{1}{2} \cdot \dfrac{1}{k^3} = \dfrac{1}{2k^3} $